Numerous state-feedback and observer designs for nonlinear dynamic systems (NDS) have been developed in the past three decades. These designs assume that NDS nonlinearities satisfy one of the following function set classifications: bounded Jacobian, Lipschitz continuity, one-sided Lipschitz, quadratic inner-boundedness, and quadratic boundedness. These function sets are characterized by constant scalars or matrices bounding the NDS' nonlinearities. These constants (i) depend on the NDS' operating region, topology, and parameters, and (ii) are utilized to synthesize observer/controller gains. Unfortunately, there is a near-complete absence of algorithms to compute such bounding constants. In this paper, we develop analytical then computational methods to compute such constants. First, for every function set classification, we derive analytical expressions for these bounding constants through global maximization formulations. Second, we utilize a derivative-free, interval-based global maximization algorithm based on branch-and-bound framework to numerically obtain the bounding constants. Third, we showcase the effectiveness of our approaches to compute the corresponding parameters on some NDS such as highway traffic networks and synchronous generator models.
Sydney Institute for Robotics and Intelligent Systems (SIRIS)（悉尼机器人与智能系统研究所）；Australian Centre for Field Robotics (ACFR)（澳大利亚野外机器人中心）；University of Sydney（悉尼大学）
This paper introduces new parameterizations of equilibrium neural networks, i.e. networks defined by implicit equations. This model class includes standard multilayer and residual networks as special cases. The new parameterization admits a Lipschitz bound during training via unconstrained optimization: no projections or barrier functions are required. Lipschitz bounds are a common proxy for robustness and appear in many generalization bounds. Furthermore, compared to previous works we show well-posedness (existence of solutions) under less restrictive conditions on the network weights and mor…
React to Surprises: Stable-by-Design Neural Feedback Control and the Youla-REN
Australian Centre for Robotics（澳大利亚机器人中心）；School of Aerospace, Mechanical and Mechatronic Engineering（航空航天、机械与机电工程学院）；The University of Sydney（悉尼大学）；Laboratory for Information and Decision Systems（信息与决策系统实验室）；Dept. Electrical Engineering and Computer Science（电气工程与计算机科学系）
This paper proposes a novel unified interval-valued observer synthesis approach for locally Lipschitz nonlinear continuous-time (CT) and discrete-time (DT) systems with nonlinear observations. A key feature of our proposed observer, which is derived using mixed-monotone decompositions, is that it is correct by construction (i.e., the true state trajectory of the system is framed by the states of the observer) without the need for imposing additional constraints and assumptions such as global Lipschitz continuity or contraction, as is done in existing approaches in the literature. Furthermore, …
LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layers
Department of Mechanical Engineering, Eindhoven University of Technology（埃因霍温理工大学机械工程系）；Institute for Systems Theory and Automatic Control, University of Stuttgart（斯图加特大学系统理论与自动控制研究所）；Australian Centre for Robotics and School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney（悉尼大学澳大利亚机器人中心及航空航天、机械与机电工程学院）
On the asymptotic hyperstability of switched systems
Institute of Research and Development of Processes, Faculty of Science and Technology University of the Basque Country（巴斯克大学科学与技术学院流程研究与开发研究所）；Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country（巴斯克大学科学与技术学院电力与电子系）；Department of Telecommunications and Systems Engineering Universitat Autònoma de Barcelona（巴塞罗那自治大学电信与系统工程系）
University of Pennsylvania（宾夕法尼亚大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；Google Brain Robotics（谷歌大脑机器人）
Inspired by the success of imitation and inverse reinforcement learning in replicating expert behavior through optimal control, we propose a learning based approach to safe controller synthesis based on control barrier functions (CBFs). We consider the setting of a known nonlinear control affine dynamical system and assume that we have access to safe trajectories generated by an expert - a practical example of such a setting would be a kinematic model of a self-driving vehicle with safe trajectories (e.g., trajectories that avoid collisions with obstacles in the environment) generated by a hum…
We address the problem of designing simultaneous input and state interval observers for Lipschitz continuous nonlinear systems with rank-deficient feedthrough, unknown inputs and bounded noise signals. Benefiting from the existence of nonlinear decomposition functions and affine abstractions, our proposed observer recursively computes the maximal and minimal elements of the estimate intervals that are proven to contain the true states and unknown inputs. Moreover, we provide necessary and sufficient conditions for the existence and sufficient conditions for the stability (i.e., uniform bounded…
This paper introduces a novel $\mathcal{H}_{\infty}$-optimal interval observer synthesis for bounded-error/uncertain locally Lipschitz nonlinear continuous-time (CT) and discrete-time (DT) systems with noisy nonlinear observations. Specifically, using mixed-monotone decompositions, the proposed observer is correct by construction, i.e., the interval estimates readily frame the true states without additional constraints or procedures. In addition, we provide sufficient conditions for input-to-state (ISS) stability of the proposed observer and for minimizing the $\mathcal{H}_{\infty}$ gain of th…
